Topological insulators are insulating materials with conducting surfaces. In this talk I will introduce topology by its application to the analysis of tie knots. I will then describe the remarkable electrostatics of topological insulators that mimics the behavior of axion domain walls studied in particle physics. Possible experiments to observe this physics will be discussed. Finally I will give a pedagogical introduction to the Su-Schrieffer model, a simple one dimensional analog of a topological insulator. My collaborators and I have proposed a photonic realization of this model that has now been observed experimentally.